The former Borussia Dortmund playmaker has struggled to establish himself at Old Trafford since his £12m move in summer 2012.
He has made just 24 Premier League starts but earned praise for his second-half display against Swansea in the Premier League last weekend, when he was moved into his favoured central position.
Kagawa told United's official website: "I think I can still improve my strength. I'm not the tallest or biggest player, so I have to move my body more.
"Smaller players in the Premier League are very good at using their bodies (to get past the opposition) and that's what I will continue to do.
"I realise the Premier League is a very tough league and I know I have to be stronger."
"Carrick and Fletcher sitting, with Rooney Kagawa and Januzaj behind RVP" -------- Personally that would be my preferred formation. The only issue is getting all of those players fit at the same time. Carrick and Fletcher have been basent for large chunks, and we're currently waiting for RvP and Rooney to return as well. Untill those players are fit, we have to make do with what we have, which means playing the likes of Valencia, Nanim, Young and Cleverley. None are woeful, but then none are consistent enough to be starting every week, in an ideal world.- HarryBoulton